A constraint-handling technique for parametric optimization and control co-design

This paper proposes a novel technique for handling constraints in population-based algorithms (e.g., genetic algorithms) for parametric optimization and control co-design (CCD). Constraint boundaries are approximated during optimization using a machine-learning classification approach called a support vector machine (SVM). Population members classified as infeasible are shifted to the predicted boundary of the feasible set, promoting exploration in the most important regions of the search space. A numerical test problem and a case study of an elastic inverted pendulum on a cart are used for benchmarking. The inverted pendulum problem, which features inherently unstable dynamics and control system limitations (i.e., saturation), highlights the relevance of constraint handling in CCD problems. The case study includes constraints to ensure stability and account for controller saturation. Performance and computational cost are compared to the existing parametric optimization technique, Predicted Parameterized Pareto Genetic Algorithm (P3GA). Results show that the P3GA with the newly proposed constraint-handling technique outperforms the original P3GA both qualitatively and quantitatively.